The design of nonrecursive digital filters via convex optimization

The advantages of optimization in filter design over strongly specialized methods based upon approximation theory are well known since some years, first of all in the area of constrained linear-phase filter design. Mainly finite linear optimization has been used which requires the discretization w.r.t. the frequency variable and, if necessary, the linearization of important nonlinear filter characteristics. The work here is founded on convex finite and semi-infinite optimization. The approach avoids the discretization step and thereby, in particular, enables the design of large filters on personal computers. Moreover, convex functions such as the magnitude response, magnitude of the complex approximation error, and some quadratic error functions can be used in their original form. (orig.)SIGLEAvailable from TIB Hannover: RR 7760(1998,3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The direct solution of nonconvex nonlinear FIR filter design problems by a SIP method

FIR filter design problems in the frequency domain are nonlinear (semi-infinite) optimization problems. In practice these almost always have been solved in a simplified form and/or only under restricting assumptions. In this paper, the four main design approximation problems in the frequency domain are stated in general forms, which allow the inclusion of constraints and the choice of an arbitrary L"p - resp. l"p-norm, 1lep#<=##infinity#, for the approximation. The careful mathematical formulation of these problems enables the derivation of several theoretical results (given in another paper), and it empowers the application of optimization procedures to their direct solution. Then, for the actual solution of these problems, a novel method for nonlinear semi-infinite programming is introduced and applied to several specific design problems. For some examples, the computed solution of the nonlinear problem is compared with a solution obtained form a convex approximation of the problem. (orig.)SIGLEAvailable from TIB Hannover: RR 7760(1999,4) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman